1. Field of the Invention
The present invention relates to a method and apparatus for analyzing a structure of a complex material layer, and a storage medium storing a program for causing a computer to execute the method.
2. Description of the Related Art
A complex material layer of a semiconductor package and a mounting substrate may be subjected to deformation such as warpage by heat. Thus, in order to enhance the reliability of a semiconductor device including a complex material layer, it is very important to analyze the degree of the deformation in the complex material layer may be deformed, in advance. The complex material layer may be analyzed by estimating the mechanical physical property values of each layer using a finite element method. However, a wiring layer included in the complex material layer has a very complicated shape in wiring. Therefore, if an attempt is made so as to model the wiring layer precisely, the model becomes too complicated. This causes inconvenience that it takes too much time to analyze a complex material layer including a precisely modeled wiring layer. In view of this, various methods of analyzing the structure of a complex material layer, which enhance efficiency in analysis, have been conceived.
JP 2004-013437 A (hereinafter, referred to as Patent Document 1) discloses a method of analyzing warpage of a substrate, capable of predicting the warpage of a substrate precisely, reflecting the difference due to the density of a wiring pattern. According to the method of analyzing warpage of a substrate, first, a plurality of elements in arbitrary shapes dividing the substrate are created based on model data representing the shape of the substrate. Then, the data on the wiring pattern to be formed on the substrate is compared with each element, to thereby calculate, for each element, the ratio at which the wiring pattern occupies the element. Then, based on the ratio for each element, at which the wiring pattern occupies the element, the mechanical physical property values are calculated for each element. Then, the warpage of the substrate is analyzed based on the mechanical physical property values for each element.
However, the inventor of the present invention has found the following problems. According to the analysis method disclosed in Patent Document 1, the physical property values of each element dividing the wiring pattern are calculated as a total obtained after the physical property values of a copper foil and the physical property values of an insulating material are prorated in accordance with the density (ratio of the copper foil) of the wiring pattern, for each element. The calculated physical property values are likely to become large in the case where the physical property values of each member vary largely, and hence, the calculated physical property values of an element may become those of properties that may not be obtained in reality. For example, an ordinary substance tends to have a small Young's modulus when a thermal expansion thereof is large, and tends to have a large Young's modulus when a thermal expansion thereof is small. In the case of copper and resin (solder resist), the thermal expansion of copper is small, whereas the Young's modulus thereof is large. On the other hand, the thermal expansion of resin is large, whereas the Young's modulus thereof is small. Accordingly, in the case where an element composed of copper and resin is analyzed, physical property values in which both the thermal expansion and the Young's modulus are large may be obtained. That is, when the method of Patent Document 1 is used, physical property values of properties that may not be obtained for an ordinary substance are obtained in each divided element, and hence, there arises a problem that the analysis results become substantially different from actually measured values.